On p-beauty contest integer games

In this paper we provide a full characterization of the pure-strategyNash Equilibria for the p-Beauty Contest Game when we restrict player schoices to integer numbers. Opposed to the case of real number choices,equilibrium uniqueness may be lost depending on the value of p and thenumber of players: in particular, as p approaches 1 any symmetric profileconstitutes a Nash Equilibrium. We also show that any experimental p-BeautyContest Game can be associated to a game with the integer restriction andthus multiplicity of equilibria becomes an issue. Finally, we show thatin these games the iterated deletion of weakly dominated strategies maynot lead to a single outcome while the iterated best-reply process alwaysdoes (though the outcome obtained depends on the initial conditions).

Causal assessment in finite extensive-form games

Two finite extensive-form games are empirically equivalent when theempirical distribution on action profiles generated by every behaviorstrategy in one can also be generated by an appropriately chosen behaviorstrategy in the other. This paper provides a characterization ofempirical equivalence. The central idea is to relate a game's informationstructure to the conditional independencies in the empirical distributionsit generates. We present a new analytical device, the influence opportunitydiagram of a game, describe how such a diagram is constructed for a givenextensive-form game, and demonstrate that it provides a complete summaryof the information needed to test empirical equivalence between two games.

Stochastic evolution of rules for playing normal form games

The evolution of boundedly rational rules for playing normal form games is studied within stationary environments ofstochastically changing games. Rules are viewed as algorithms prescribing strategies for the different normal formgames that arise. It is shown that many of the folk results of evolutionary game theory typically obtained witha fixed game and fixed strategies carry over to the present case. The results are also related to recent experimentson rules and games.

Max-convex decompositions for cooperative TU games

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with non-negative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition

A characterization of a new value and an existing value for cooperative games with levels structure of cooperation

En aquest treball presentem dues caracteritzacions de dos valors diferents en el marc dels jocs coalicionals amb cooperació restringida. Les restriccions són introduïdes com una seqüència finita de particions del conjunt del jugadors, de manera que cada una d'elles eés més grollera que l'anterior, formant així una estructura amb diferents nivells d'unions a priori.

Von Neumann-Morgenstern solution and convex descompositions of TU games

We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas¿ five player game with a unique stable set different from the core, are reckoning and analyzed.

The Lorenz-maximal core allocations and the kernel in some classes of assignment games

En aquest treball demostrem que en la classe de jocs d'assignació amb diagonal dominant (Solymosi i Raghavan, 2001), el repartiment de Thompson (que coincideix amb el valor tau) és l'únic punt del core que és maximal respecte de la relació de dominància de Lorenz, i a més coincideix amb la solucié de Dutta i Ray (1989), també coneguda com solució igualitària. En segon lloc, mitjançant una condició més forta que la de diagonal dominant, introduïm una nova classe de jocs d'assignació on cada agent obté amb la seva parella òptima almenys el doble que amb qualsevol altra parella. Per aquests jocs d'assignació amb diagonal 2-dominant, el repartiment de Thompson és l'únic punt del kernel, i per tant el nucleolo.

Monge assignment games

Un juego de asignación se define por una matriz A; donde cada fila representa un comprador y cada columna un vendedor. Si el comprador i se empareja a un vendedor j; el mercado produce aij unidades de utilidad. Estudiamos los juegos de asignación de Monge, es decir, aquellos juegos bilaterales de asignación en los cuales la matriz satisface la propiedad de Monge. Estas matrices pueden caracterizarse por el hecho de que en cualquier submatriz 2x2 un emparejamiento óptimo está situado en la diagonal principal. Para mercados cuadrados, describimos sus núcleos utilizando sólo la parte central tridiagonal de elementos de la matriz. Obtenemos una fórmula cerrada para el reparto óptimo de los compradores dentro del núcleo y para el reparto óptimo de los vendedores dentro del núcleo. Analizamos también los mercados no cuadrados reduciéndolos a matrices cuadradas apropiadas.

On the nucleolus of 2 x 2 assignment games

[spa] En este artículo hallamos fórmulas para el nucleolo de juegos de asignación arbitrarios con dos compradores y dos vendedores. Se analizan cinco casos distintos, dependiendo de las entradas en la matriz de asignación. Los resultados se extienden a los casos de juegos de asignación de tipo 2 x m o m x 2.

Aggregate monotonic stable single-valued solutions for cooperative games

[cat] En aquest treball caracteritzem les solucions puntuals de jocs cooperatius d'utilitat transferible que compleixen selecció del core i monotonia agregada. També mostrem que aquestes dues propietats són compatibles amb la individualitat racional, la propietat del jugador fals i la propietat de simetria. Finalment, caracteritzem les solucions puntuals que compleixen les cinc propietats a l'hora.

The maximun and the addition of assigment games

[cat] En el context dels mercats a dues bandes, considerem, en primer lloc, que els jugadors poden escollir on dur a terme les seves transaccions. Mostrem que el joc corresponent a aquesta situació, que es representa pel màxim d’un conjunt finit de jocs d’assignació, pot ser un joc no equilibrat. Aleshores proporcionem condicions per a l’equilibri del joc i, per aquest cas, analitzem algunes propietats del core del joc. En segon lloc, considerem que els jugadors poden fer transaccions en diversos mercats simultàniament i, llavors, sumar els guanys obtinguts. El joc corresponent, representat per la suma d’un conjunt finit de jocs d’assignació, és equilibrat. A més a més, sota certes condicions, la suma dels cores dels dos jocs d’assignació coincideix amb el core del joc suma.

Coalitionally monotonic set-solutions for cooperative TU games

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional monotonicity. As the main result, it is showed that coalitional monotonicity is not only incompatible with the core-selection property but also with the bargaining-selection property. This new impossibility result reinforces the tradeoff between these kinds of interesting and intuitive economic properties. Positive results about compatibility between desirable economic properties are given replacing the core selection requirement by the core-extension property.

A Note on Shapley's convex measure games

L. S. Shapley, in his paper 'Cores of Convex Games', introduces Convex Measure Games, those that are induced by a convex function on R, acting over a measure on the coalitions. But in a note he states that if this function is a function of several variables, then convexity for the function does not imply convexity of the game or even superadditivity. We prove that if the function is directionally convex, the game is convex, and conversely, any convex game can be induced by a directionally convex function acting over measures on the coalitions, with as many measures as players

Security strategies and equilibria in multiobjetives matrix games

Multiobjective matrix games have been traditionally analyzed from two different points of view: equiibrium concepts and security strategies. This paper is based upon the idea that both players try to reach equilibrium points playing pairs of security strategies, as it happens in scalar matrix games. We show conditions guaranteeing the existence of equilibria in security strategies, named security equilibria

All assignment games with the same core have the same nucleolus

There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyer-seller exact representative